The weighted hardy inequality: New proofs and the case p=1

被引：132

作者：

Sinnamon, G ^{[1
]}

Stepanov, VD ^{[1
]}

机构：

[1] RUSSIAN ACAD SCI, COMP CTR FAR EASTERN BRANCH, KHABAROVSK 680042, RUSSIA

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 1996年 / 54卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

D O I：

10.1112/jlms/54.1.89

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An elementary proof is given of the weight characterisation for the Hardy inequality [GRAPHICS] in the case 0 < q < p, 1 < p < infinity. It is also shown that certain weighted inequalities with monotone kernels are equivalent to inequalities in which one of the weights is monotone. Using this, a characterisation of those weights for which (1.1) holds with 0 < q < 1 = p is given. Results for (1.1), considered as an inequality over monotone functions f are presented.

引用

页码：89 / 101

页数：13

共 12 条

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